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Laser ultrasound was used to determine dispersion curves of surface acoustic waves on a Si (001) surface covered by AlScN films with a scandium content between 0 and 41%. By including off-symmetry directions for wavevectors, all five independent elastic constants of the film were extracted from the measurements. Results for their dependence on the Sc content are presented and compared to corresponding data in the literature, obtained by alternative experimental methods or by ab-initio calculations.
Micro-cracks give rise to non-analytic behavior of the stress-strain relation. For the case of a homogeneous spatial distribution of aligned flat micro-cracks, the influence of this property of the stress-strain relation on harmonic generation is analyzed for Rayleigh waves and for acoustic wedge waves with the help of a simple micromechanical model adopted from the literature. For the efficiencies of harmonic generation of these guided waves, explicit expressions are derived in terms of the corresponding linear wave fields. The initial growth rates of the second harmonic, i.e., the acoustic nonlinearity parameter, has been evaluated numerically for steel as matrix material. The growth rate of the second harmonic of Rayleigh waves has also been determined for microcrack distributions with random orientation, using a model expression for the strain energy in terms of strain invariants known in a geophysical context.
Propagation of acoustic waves is considered in a system consisting of two stiff quarter-spaces connected by a planar soft layer. The two quarter-spaces and the layer form a half-space with a planar surface. In a numerical study, surface waves have been found and analyzed in this system with displacements that are localized not only at the surface, but also in the soft layer. In addition to the semi-analytical finite element method, an alternative approach based on an expansion of the displacement field in a double series of Laguerre functions and Legendre polynomials has been applied.
It is shown that a number of branches of the mode spectrum can be interpreted and remarkably well described by perturbation theory, where the zero-order modes are the wedge waves guided at a rectangular edge of the stiff quarter-spaces or waves guided at the edge of a soft plate with rigid surfaces.
For elastic moduli and densities corresponding to the material combination PMMA–silicone–PMMA, at least one of the branches in the dispersion relation of surface waves trapped in the soft layer exhibits a zero-group velocity point.
Potential applications of these 1D guided surface waves in non-destructive evaluation are discussed.
In numerical calculations, guided acoustic waves, localized in two spatial dimensions, have been shown to exist and their properties have been investigated in three different geometries, (i) a half-space consisting of two elastic media with a planar interface inclined to the common surface, (ii) a wedge made of two elastic media with a planar interface, and (iii) the free edge of an elastic layer between two quarter-spaces or two wedge-shaped pieces of a material with elastic properties and density differing from those of the intermediate layer.
For the special case of Poisson media forming systems (i) and (ii), the existence ranges of these 1D guided waves in parameter space have been determined and found to strongly depend on the inclination angle between surface and interface in case (i) and the wedge angle in case (ii). In a system of type (ii) made of two materials with strong acoustic mismatch and in systems of type (iii), leaky waves have been found with a high degree of spatial localization of the associated displacements, although the two materials constituting these structures are isotropic.
Both the fully guided and the leaky waves analyzed in this work could find applications in non-destructive evaluation of composite structures and should be accounted for in geophysical prospecting, for example.
A critical comparison is presented of the two computational approaches employed, namely a semi-analytical finite element scheme and a method based on an expansion of the displacement field in a double series of special functions.
Among the various types of guided acoustic waves, acoustic wedge waves are non-diffractive and non-dispersive. Both properties make them susceptible to nonlinear effects. Investigations have recently been focused on effects of second-order nonlinearity in connection with anisotropy. The current status of these investigations is reviewed in the context of earlier work on nonlinear properties of two-dimensional guided acoustic waves, in particular surface waves. The role of weak dispersion, leading to solitary waves, is also discussed. For anti-symmetric flexural wedge waves propagating in isotropic media or in anisotropic media with reflection symmetry with respect to the wedge’s mid-plane, an evolution equation is derived that accounts for an effective third-order nonlinearity of acoustic wedge waves. For the kernel functions occurring in the nonlinear terms of this equation, expressions in terms of overlap integrals with Laguerre functions are provided, which allow for their quantitative numerical evaluation. First numerical results for the efficiency of third-harmonic generation of flexural wedge waves are presented.
Surface acoustic waves are propagated toward the edge of an anisotropic elastic medium (a silicon crystal), which supports leaky waves with a high degree of localization at the tip of the edge. At an angle of incidence corresponding to phase matching with this leaky wedge wave, a sharp peak in the reflection coefficient of the surface wave was found. This anomalous reflection is associated with efficient excitation of the leaky wedge wave. In laser ultrasound experiments, surface acoustic wave pulses were excited and their reflection from the edge of the sample and their partial conversion into leaky wedge wave pulses was observed by optical probe-beam deflection. The reflection scenario and the pulse shapes of the surface and wedge-localized guided waves, including the evolution of the acoustic pulse traveling along the edge, have been confirmed in detail by numerical simulations.
Nonlinear acoustic waves are considered that have displacements localized at the tip of an elastic wedge. The evolution equation governing their propagation is discussed and compared with its analogues pertaining to nonlinear acoustic surface and bulk waves. Solitary wave solutions of the evolution equation have been determined numerically for the cases of two rectangular edges which may be viewed as generated by splitting a half-space, consisting of crystalline silicon, into two quarter-spaces. For these two geometries, the kernel in the nonlinear terms of the evolution equation has been calculated from the second-order and third-order elastic constants of silicon, and weak dispersion due to tip truncation has been considered. Solitary pulse shapes have been computed and collisions of solitary pulses have been simulated for various relative speeds of the two collision partners. Collision scenarios for the two wedge geometries were found to differ considerably. Special attention is paid to the peculiar interaction of two initially identical solitary pulses.
A laser-operated, angle-tunable transducer was employed to excite selectively elastic waves guided along the apex of a solid wedge. The propagation of wedge waves at anisotropic monocrystalline silicon edges with different symmetry properties was studied by optical detection. The reduced symmetry in crystals, as compared to isotropic media, causes a number of new features, such as the existence of supersonic leaky wedge waves, tilted spatial pulse profiles, and other peculiarities of their localization. Experimental and theoretical results are presented for three different types of symmetry configurations: the wedge symmetric about its midplane, the wedge symmetric about the plane normal to its apex line, and the wedge symmetric about one of its faces. The experiments include accurate measurements of the phase velocity and the wave field distribution, providing information on localization and coupling of wedge waves with other waves. Theoretically, the wedge waves were treated by the Laguerre function method, extended to modes that are not localized at the tip of the wedge. This approach allowed an accurate description of the observed localized and leaky wedge waves in anisotropic wedges.
Acoustic waves are investigated which are guided at the edge (apex line) of a wedge-shaped elastic body or at the edge of an elastic plate. The edges contain a periodic sequence of modifications, consisting either of indentations or inclusions with a different elastic material which gives rise to high acoustic mismatch. Dispersion relations are computed with the help of the finite element method. They exhibit zero-group velocity points on the dispersion branches of edge-localized acoustic modes. These special points also occur at Bloch-Floquet wavenumbers away from the Brillouin zone boundary. Deep indentations lead to flat branches corresponding to largely non-interacting, Einstein-oscillator like vibrations of the tongues between the grooves of the periodic structure. Due to the nonlinearity of the elastic media, quantified by their third-order elastic constants, an acoustic mode localized at a periodically modified edge generates a second harmonic which partly consists of surface and plate modes propagating into the elastic medium in the direction vertical to the edge. This acoustic radiation at the second-harmonic frequency is investigated for an elastic plate and a truncated sharp-angle wedge with periodic inclusions at their edges. Unlike nonlinear bulk wave generation by surface acoustic waves in an interdigital structure, surface and plate mode radiation by edge-localized modes can be visualized directly in laser-ultrasound experiments.
The laser ultrasound (LU) technique has been used to determine dispersion curves for surface acoustic waves (SAW) propagating in AlScN/Al2O3 systems. Polar and non-polar Al0.77Sc0.23N thin films were prepared by magnetron sputter epitaxy on Al2O3 substrates and coated with a metal layer. SAW dispersion curves have been measured for various propagation directions on the surface. This is easily achieved in LU measurements since no additional surface structures need to be fabricated, which would be required if elastic properties are determined with the help of SAW resonators. Variation of the propagation direction allows for efficient use of the system’s anisotropy when extracting information on elastic properties. This helps to overcome the complexity caused by a large number of elastic constants in the film material. An analysis of the sensitivity of the SAW phase velocities (with respect to the elastic moduli and their dependence on SAW propagation direction) reveals that the non-polar AlScN films are particularly well suited for the extraction of elastic film properties. Good agreement is found between experiment and theoretical predictions, validating LU as a non-destructive and fast technique for the determination of elastic constants of piezoelectric thin films.